Product-moment correlation, unweighted/weighted correlation and covariance matrix, allows variables to be disregarded

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NAG[g02bxc] NAG[nag_corr_cov] - Product-moment correlation, unweighted/weighted correlation and covariance matrix, allows variables to be disregarded

Calling Sequence

g02bxc(x, sw, wmean, std, r, v, 'n'=n, 'm'=m, 'tdx'=tdx, 'sx'=sx, 'wt'=wt, 'tdr'=tdr, 'tdv'=tdv, 'fail'=fail)

nag_corr_cov(. . .)

Parameters

x - Matrix(1..n, 1..tdx, datatype=float[8], order=C_order);

On entry: the data must contain the th observation on the th variable, , for ; .

sw - assignable;

Note: On exit the variable sw will have a value of type float.

On exit: the sum of weights if wt is not the null pointer, otherwise sw contains the number of observations, .

wmean - Vector(1..m, datatype=float[8]);

On exit: the sample means. contains the mean for the th variable.

std - Vector(1..m, datatype=float[8]);

On exit: the standard deviations. contains the standard deviation for the th variable.

r - Matrix(1..m, 1..tdr, datatype=float[8], order=C_order);

On exit: the matrix of Pearson product-moment correlation coefficients. contains the correlation between variables and , for .

v - Matrix(1..m, 1..tdv, datatype=float[8], order=C_order);

On exit: the variance-covariance matrix. contains the covariance between variables and , for .

'n'=n - integer; (optional)

Default value: the first dimension of the arrays x, wt.

On entry: the number of observations in the data set, .

Constraint: . .

'm'=m - integer; (optional)

Default value: the first dimension of the arrays sx, wmean, std, r, v and the second dimension of the arrays sx, wmean, std, r, vthe arrays x, r, v.

On entry: the total number of variables, .

Constraint: . .

'tdx'=tdx - integer; (optional)

On entry: the second dimension of the array x as declared in the function from which nag_corr_cov (g02bxc) is called.

Constraint: . .

'sx'=sx - Vector(1..m, datatype=integer[kernelopts('wordsize')/8]); (optional)

On entry: indicates which variables to include in the analysis.

The th variable is to be included.

The th variable is not to be included.

sx is set to the null pointer (Integer *)0 All variables are included in the analysis, i.e., .

Constraint: , for . .

'wt'=wt - Vector(1..n, datatype=float[8]); (optional)

On entry: the optional frequency weighting for each observation. contains the weight for the th data value. Usually will be an integral value corresponding to the number of observations associated with the th data value, or zero if the th data value is to be ignored. If wt is set to the null pointer (double *)0 then wt is not referenced.

Constraint: , for . .

'tdr'=tdr - integer; (optional)

On entry: the second dimension of the array r as declared in the function from which nag_corr_cov (g02bxc) is called.

Constraint: . .

'tdv'=tdv - integer; (optional)

On entry: the second dimension of the array v as declared in the function from which nag_corr_cov (g02bxc) is called.

Constraint: . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_corr_cov (g02bxc) calculates the Pearson product-moment correlation coefficients and the variance-covariance matrix for a set of data. Weights may be used.

Description

For observations on variables a one-pass updating algorithm (see West (1979)) is used to compute the means, the standard deviations, the variance-covariance matrix, and the Pearson product-moment correlation matrix for selected variables. Suitables weights may be used to indicate multiple observations and to remove missing values. The quantities are defined by:

(a) The means

(b) The variance-covariance matrix

C[jk]=((∑)w[i](x[ij],-,(x)[j])(x[ik],-,(x)[k]))/((∑)w[i]-1) j,k=1,..,p

(d) The Pearson product-moment correlation coefficients

R[j*k] = C[j*k]*j/sqrt(C[j*j]*C[k*k]), k = 1, () .. (), p

where is the value of the th observation on the th variable and is the weight for the th observation which will be 1 in the unweighted case.

Note that the denominator for the variance-covariance is , so the weights should be scaled so that the sum of weights reflects the true sample size.

Error Indicators and Warnings

"NE_ALLOC_FAIL"

Dynamic memory allocation failed.

"NE_INT_ARG_LE"

On entry, n must be greater than 1: .

"NE_INT_ARG_LT"

On entry, m must not be less than 1: .

"NE_NEG_SX"

On entry, at least one element of sx is negative.

"NE_NEG_WEIGHT"

On entry, at least one of the weights is negative.

"NE_POS_SX"

On entry, no element of sx is positive.

"NE_SW_LT_ONE"

On entry, the sum of weights is less than 1.0.

"NE_VAR_EQ_ZERO"

A variable has zero variance. At least one variable has zero variance. In this case v and std are as calculated, but r will contain zero for any correlation involving a variable with zero variance.

	Accuracy
	For a discussion of the accuracy of the one pass algorithm see Chan et al. (1982) and West (1979).

	Further Comments
	Correlation coefficients based on ranks can be computed using g02brc (nag_ken_spe_corr_coeff).

Examples

n := 3:
m := 3:
tdx := 3:
tdr := 3:
tdv := 3:
x := Matrix([[0.931, 0.09, 0.887], [0.0009, 0.009900000000000001, 0.0999], [0.13, 1.307, 0.37]], datatype=float[8], order='C_order'):
sx := Vector([], datatype=integer[kernelopts('wordsize')/8]):
wt := Vector([9.123100000000001, 3.7011, 4.523], datatype=float[8]):
wmean := Vector(3, datatype=float[8]):
std := Vector(3, datatype=float[8]):
r := Matrix(3, 3, datatype=float[8], order='C_order'):
v := Matrix(3, 3, datatype=float[8], order='C_order'):
NAG:-g02bxc(x, sw, wmean, std, r, v, 'n' = n, 'm' = m, 'tdx' = tdx, 'sx' = sx, 'wt' = wt, 'tdr' = tdr, 'tdv' = tdv):

sw;

wmean;

std;

	See Also
	Chan T F, Golub G H and Leveque R J (1982) Updating Formulae and a Pairwise Algorithm for Computing Sample Variances Compstat, Physica-Verlag West D H D (1979) Updating mean and variance estimates: An improved method Comm. ACM 22 532–555 g02 Chapter Introduction. NAG Toolbox Overview. NAG Web Site.